Find the Area of the Portion of the Surface $f ( x , y ) = \sqrt { 12 - x ^ { 2 } - y ^ { 2 } } \text { that lies above }$

Multiple Choice

Find the area of the portion of the surface $f ( x , y ) = \sqrt { 12 - x ^ { 2 } - y ^ { 2 } } \text { that lies above }$ the region $R = \left\{ ( x , y ) : x ^ { 2 } + y ^ { 2 } \leq 144 \right\}$ Round your answer to two decimal places.

A) 144.00
B) 118.44
C) 904.78
D) 452.39
E) 1,421.22